Criterion minimum image

The computer simulations employed the molecular dynamics technique, in which particles are moved deterministically by integrating their equations of motion. The system size was 864 Lennard-Jones atoms, of which one was the solute (see Table II for potential parameters). There were no solute-solute interactions. Periodic boundary conditions and the minimum image criterion were used (76). The cutoff radius for binary interactions was 3.5 G (see Table II). Potentials were truncated beyond the cutoff. 

This limitation on the resolution of images by diffraction is quantified in terms of the so-caUed Rayleigh criterion the imaging process is said to be diffraction limited when the first diffraction minimum of the image of one source point coincides with the maximum of a neighbouring one. The numerical value for the Rayleigh diffraction angle A0r, is... 

Periodic boundary conditions refer to the simulation of structures consisting of a periodic lattice of identical subunits. Periodic boundaries help simulate bulk-material, solvent, and crystalline systems. Ideally, a periodic system infinitely replicates in all dimensions to form a periodic lattice. However, in practice, all periodic boundary algorithms imply a cutoff criterion for computational efficiency (Figure 1.1). In these cutoff schemes, each atom interacts with the nearest images of other N - I atoms (minimum-image convention) or only with the explicit images contained in a sphere... 

The resolution or "resolving power" of a light microscope is usually specified as the minimum distance between two lines or points in the imaged object, at which they will be perceived as separated by the observer. The Rayleigh criterion [42] is extensively used in optical microscopy for determining the resolution of light microscopes. It imposes a resolution limit. The criterion is satisfied, when the centre of the Airy disc for the first object occurs at the first minimum of the Airy disc of the second. This minimum distance r can then be calculated by Equation (3). 

In 1873, Ernst Abbe established the resolution limit of optical microscopes The minimum distance, d, between two structural elements to be imaged as two objects instead of one is given by d = A/(2 NA), where X is the wavelength of light and NA the numerieal aperture of the objective lens. The physical root for resolution limit is related to optical diffraction and loss of evanescent waves in far-field the evaneseent waves carry high-frequency subwavelength spatial information of an object and decay exponentially with distance from the objeet. With white lights, optical microscope resolution is limited at about 200-250 nm. For about one hundred years, the Abbe criterion was considered the fundamental limit of optical microscope resolution. 

According to the Rayleigh criterion, two equally intense spectral lines with wavelengths X and X -f AX are just resolved if the central diffraction maximum of S2(A.) coincides with the first minimum of S2(A +AA) (see above). This means that their maxima are just separated by = F2(X/a), From (4.6) one can compute that, in this case, both lines partly overlap with a dip of (8/71 )/max 0.8/max between the two maxima. The distance between the centers of the two slit images is then obtained from (4.7) (see Fig. 4.9b) as... 

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